An ultrasound-based method and apparatus for characterizing sample porosity

Abstract

This specification relates to the field of ultrasonic technology, and more particularly to a method and apparatus for characterizing sample porosity based on ultrasound. The method includes: obtaining a measured total attenuation curve of the sample experimentally; equipping the three-phase mixed medium of the sample with an isotropic homogeneous medium to obtain a three-phase porosity elastic control equation; wherein the three-phase mixed medium of the sample includes: a sample mineral phase, an intrapore cellular solid phase, and a pore fluid phase; the three-phase porosity elastic control equation describes the dissipation of coupling between the pore fluid and the sample; calculating the total attenuation of the ultrasonic signal passing through the sample based on the three-phase porosity elastic control equation; and comparing the total attenuation with the measured total attenuation curve to determine the porosity of the sample. Using the embodiments of this specification, the porosity of the sample can be inverted to obtain porosity parameters for imaging ultrasonic detection data.

Description

Technical Field

[0001] This specification relates to the field of ultrasonic technology, and in particular to an ultrasonic-based method and apparatus for characterizing sample porosity. Background Technology

[0002] Due to its core advantages such as low cost, non-invasiveness, no radiation, and real-time imaging, ultrasound imaging equipment is now widely used in the diagnosis of various diseases. Ultrasound waves have good tissue penetration, making them suitable for transcranial ultrasound brain imaging through the skull. However, in current transcranial ultrasound brain imaging and neuromodulation processes, the propagation mechanism of ultrasound waves within the intact skull lacks accurate physical modeling and quantitatively invertible parameter characterization. This leads to attenuation compensation and phase correction relying on empirical methods, making it difficult to guarantee image quality and field distribution control.

[0003] How to accurately characterize the porosity of a sample during bone ultrasound testing is a problem that urgently needs to be solved. Summary of the Invention

[0004] To address the problems in the prior art, this specification provides an ultrasonic-based method and apparatus for characterizing sample porosity, which solves the problem that the prior art cannot accurately characterize sample porosity.

[0005] This specification provides an ultrasonic-based method for characterizing sample porosity, including: The measured total decay curve of the sample was obtained through experiments; The three-phase mixed medium of the sample is equivalent to an isotropic homogeneous medium, resulting in a three-phase porosity elastic control equation. The three-phase mixed medium of the sample includes: a sample mineral phase, an intrapore cellular solid phase, and a pore fluid phase. The three-phase porosity elastic control equation is used to describe the dissipation of the coupling between the pore fluid and the sample. The total attenuation of the ultrasonic signal after passing through the sample is calculated based on the three-phase aperture elastic control equation. The porosity of the sample is determined by comparing the total attenuation with the measured total attenuation curve.

[0006] As a further aspect of this specification, the three-phase mixed medium of the sample is equivalent to an isotropic homogeneous medium, resulting in the following further inclusion in the three-phase porosity elastic control equation: The three-phase aperture elastic control equations include the frequency-dependent mass matrix, damping matrix, and elastic recovery operator matrix of the sample.

[0007] As a further aspect of this specification, the frequency-dependent fluid-structure drag coefficients are constructed using the Biot-JKD model, the Biot low-frequency model, the dynamic tortuosity / dynamic permeability model, or the Biot-Stoll model, thereby forming the damping matrix.

[0008] As a further aspect of this specification, the coupling between the pore fluid and the sample includes viscous dissipation and tortuosity effects.

[0009] As a further aspect of this specification, the three-phase mixed medium of the sample is equivalent to an isotropic homogeneous medium, resulting in the following further inclusion in the three-phase porosity elastic control equation: Based on the Biot–JKD model, the frequency-dependent dynamic penetration rate is obtained; Substituting the dynamic permeability into the fluid-solid drag term yields the frequency-dependent fluid-solid drag coefficient.

[0010] As a further aspect of this specification, the calculation of the total attenuation of the ultrasonic signal through the sample, based on the three-phase aperture elastic control equation, further includes: Based on the volume fractions and single-phase elastic moduli of the sample mineral phase, cellular solid phase within the pores, and pore fluid phase, the equivalent bulk modulus, equivalent shear modulus, and equivalent mass density, which are equivalent to an isotropic homogeneous medium, are calculated. Substituting the equivalent bulk modulus, equivalent shear modulus, and equivalent mass density into the wave velocity-related formula yields the equivalent volume wave phase velocity, which includes the elastic longitudinal wave velocity. For a given frequency, substitute the plane wave solution into the three-phase aperture elastic control equation, and set the determinant of the coefficient matrix of the three-phase aperture elastic control equation to zero to obtain the complex dispersion equation of the propagation mode. Solving the complex dispersion equation yields the complex wave number; wherein, the real part of the complex wave number describes the spatial propagation characteristics of the wave and determines the phase velocity of the wave, the phase velocity being constrained by the elastic longitudinal wave velocity of the equivalent volume wave phase velocity, and the imaginary part of the complex wave number describes the amplitude attenuation characteristics of the wave and determines the intrinsic attenuation of the wave after passing through the sample.

[0011] As a further aspect of this specification, based on Bruggeman's effective medium theory, the equivalent bulk modulus, equivalent shear modulus, and equivalent mass density of the sample, equivalent to an isotropic homogeneous medium, are calculated using the volume fractions and single-phase elastic moduli of the sample's mineral phase, cellular solid phase within the pores, and pore fluid phase.

[0012] As another further aspect of this specification, the wave speed-related relationship is determined according to the generalized Hooke's law.

[0013] As a further aspect of this specification, the calculation of the total attenuation of the ultrasonic signal through the sample, based on the three-phase aperture elastic control equation, further includes: Based on the scattering loss caused by the sample in the high-frequency band of the ultrasonic signal, a scattering attenuation is constructed; The total attenuation is formed by combining the scattering attenuation and the intrinsic attenuation.

[0014] As a further aspect of this specification, comparing the total attenuation with the measured total attenuation curve to determine the porosity of the sample further includes: The total attenuation is fitted to the measured total attenuation curve, and an objective function is constructed with the goal of minimizing the error. The porosity corresponding to the minimum objective function is taken as the porosity of the sample.

[0015] This specification also provides an ultrasound-based sample porosity characterization device, comprising: Experimental unit, used to obtain the measured total decay curve of the sample through experiments; The three-phase porosity elastic control equation generation unit is used to convert the three-phase mixed medium of the sample into an isotropic homogeneous medium to obtain the three-phase porosity elastic control equation. The calculation unit is used to calculate the total attenuation of the ultrasonic signal after passing through the sample according to the three-phase aperture elastic control equation; The inversion unit is used to compare the total attenuation with the measured total attenuation curve to determine the porosity of the sample.

[0016] This specification also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the method described above.

[0017] This specification also provides a computer-readable storage medium storing computer instructions that, when executed by a processor, implement the above-described method.

[0018] This specification also provides a computer program product, which includes a computer program that, when executed by a processor, implements the above-described method.

[0019] Using the embodiments in this specification, the porosity of a sample can be inverted to obtain porosity parameters, which are beneficial for imaging ultrasonic detection data. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments or prior art of this specification, the drawings used in the description of the embodiments or prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this specification. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0021] Figure 1 The diagram shown is a flowchart of an ultrasound-based sample porosity characterization method according to an embodiment of this specification. Figure 2 The diagram shown is a detailed flowchart of the ultrasonic-based sample porosity characterization method according to an embodiment of this specification. Figure 3 The diagram shown is a schematic of the sound field data acquisition and processing system according to an embodiment of this specification; Figure 4 The diagram shown is a schematic representation of an ultrasound-based sample porosity characterization device according to an embodiment of this specification. Figure 5 This is a computer device provided as an embodiment of the present specification.

[0022] [Explanation of Labels in the Attached Image]

[0023] 301. Sink; 302. Ultrasonic controller; 303. Ultrasonic generator; 304. Sample fixing unit; 305. Hydrophone; 306. High-precision mobile platform; 307. Data processing device; 401. Experimental Unit; 402. Three-phase hole elastic control equation generation unit; 403. Calculation Unit; 404, Inversion Unit; 502. Computer equipment; 504, Processor; 506. Memory; 508. Drive mechanism; 510. Input / output module; 512. Input devices; 514. Output devices; 516. Presentation equipment; 518. Graphical User Interface; 520. Network interface; 522. Communication link; 524. Communication bus. Detailed Implementation

[0024] The technical solutions in the embodiments of this specification will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this specification, and not all embodiments. Based on the embodiments in this specification, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this specification.

[0025] When using ultrasound to image bones such as the skull, the skull exhibits significant heterogeneity, anisotropy, and a porous microstructure, composed of mineralized bone matrix, trabecular-cytoskeleton, and pores filled with bone marrow and interstitial fluid. This complex microstructure causes significant viscous dissipation, tortuosity loss, and high-frequency scattering in the MHz band, leading to strong attenuation, waveform distortion, and phase mismatch of ultrasound waves. This results in decreased contrast, reduced resolution, and increased artifacts in transcranial beamforming and image reconstruction. If these effects are roughly corrected using the assumption of uniform sound velocity, a simplified two-phase Biot model, or an empirical phase screen, it is difficult to quantitatively correlate attenuation and phase distortion with explicit microstructural parameters such as porosity, permeability, and tortuosity of bone tissue. This makes it impossible to provide a reliable theoretical basis for transcranial compensation, bone parametric imaging, and treatment planning.

[0026] Existing methods for constructing acoustic models of the skull based on Biot theory suffer from two serious problems. First, most transcranial ultrasound modeling and compensation methods simplify the skull into a homogeneous isotropic medium or a two-phase porous medium of "bone minerals-porous fluid," providing only equivalent sound velocity, density, and attenuation coefficients at the macroscopic level. This makes it difficult to explicitly characterize the true three-phase microstructure of the coexistence of mineralized matrix, trabecular-cytoskeleton, and pore fluid. Furthermore, they fail to adequately depict the combined effects of viscous dissipation, tortuosity, and high-frequency scattering mechanisms, resulting in inconsistencies between the prediction of P-wave (elastic longitudinal wave) phase velocity and frequency-related attenuation and the actual behavior of ex vivo skulls in the medium to high porosity range. Second, they fail to establish a quantitative mapping relationship between microstructural parameters such as skull porosity, permeability, and tortuosity and sound velocity-frequency-related attenuation. They also lack systematic calibration and uncertainty analysis combined with experiments, making it difficult to deduce physically meaningful effective porosity from measured data.

[0027] This specification provides an ultrasound-based method for characterizing sample porosity, which can obtain the microstructural parameter of a sample—porosity—with high accuracy, providing a reliable physical basis for ultrasound compensation and neural modulation. Figure 1The diagram shows a flowchart of an ultrasound-based sample porosity characterization method according to an embodiment of this specification. The diagram describes a method for calculating sample porosity based on experimental attenuation results from ultrasonic testing and calculated attenuation results considering the characteristics of the sample's mineral phase, cellular solid phase within the pores, and pore fluid phase. The method uses a three-phase porosity elastic control equation that reflects the three-phase characteristics of the sample to describe the dissipation of the coupling between the pore fluid and the sample, accurately describing the correlation between the sample's porosity and the frequency of the ultrasonic testing signal. This allows for the inversion of sample porosity. The specific methods include: Step 101: Obtain the measured total attenuation curve of the sample through experiments; Step 102: The three-phase mixed medium of the sample is equivalent to an isotropic homogeneous medium to obtain the three-phase porosity elastic control equation; wherein, the three-phase mixed medium of the sample includes: sample mineral phase, cellular solid phase within the pores and pore fluid phase; the three-phase porosity elastic control equation is used to describe the dissipation of the coupling between the pore fluid and the sample; Step 103: Calculate the total attenuation of the ultrasonic signal after passing through the sample according to the three-phase aperture elastic control equation; Step 104: Compare the total attenuation with the measured total attenuation curve to determine the porosity of the sample.

[0028] The methods described in the embodiments of this specification can be used to invert the porosity of a sample (especially bone) and obtain porosity parameters to facilitate the imaging of ultrasonic detection data.

[0029] like Figure 2 The diagram shows a detailed flowchart of the ultrasound-based bone sample porosity characterization method according to an embodiment of this specification. The diagram details the steps of the ultrasound-based bone sample porosity characterization method. The order of each step may not necessarily be as shown in the diagram; the order can be changed, and not all steps are essential. Omitting some steps may achieve the same or similar effect. In other embodiments, the bone sample may also be a biomimetic porous material, porous ceramic / polymer, etc. The method of this embodiment includes: Step 201: Acquire the time-domain signal of the reference sound field under the condition of no sample.

[0030] In this step, it can be done as follows: Figure 3The diagram shows a sound field data acquisition and processing system according to an embodiment of this specification. It includes a water tank 301, an ultrasonic controller 302, an ultrasonic generator 303, a sample fixing unit 304, a hydrophone 305, a high-precision moving platform 306, and a data processing device 307. The water tank 301 contains only deaerated and deionized water. Under the control of the ultrasonic controller 302, the ultrasonic generator 303 emits plane waves at different center frequencies in the water tank 301 to measure the sound field of the pure water environment (no sample is present in the sample fixing unit 304). The data processing device 307 controls the high-precision moving platform 306 to move in the X, Y, and Z dimensions. The hydrophone 305, located on the high-precision moving platform 306, performs spatial scanning acquisition of the reference sound field to obtain three-dimensional sound pressure data. The data processing device 307 performs spectral analysis and interface and diffraction correction on the acquired sound field data to obtain frequency domain pure water reference sound field data, which serves as the baseline for subsequent transmission attenuation calculations.

[0031] In other embodiments, other equivalent sound field measurement devices (such as mechanical scanning systems, electronic scanning arrays, hydrophone arrays, etc.) can be used as alternatives, as long as they can obtain equivalent time / frequency domain sound field data.

[0032] Step 202: Under the same environmental parameters, acquire the time-domain signal of the transmitted sound field containing the bone sample.

[0033] In this step, only deaerated deionized water is retained in the water tank 301. A bone sample (e.g., skull) is added to the bone sample fixing unit 304 and fixed between the ultrasonic generator 303 and the hydrophone 305, maintaining coaxial alignment and a fixed propagation distance. The plane wave excitation and three-dimensional scanning process are repeated to acquire the time-domain signal of the transmitted sound field. The acquired time-domain data is subjected to a signal analysis method consistent with the reference sound field to extract the first fast compression mode (P1) waveform.

[0034] Step 203: Obtain the measured total attenuation curve of the bone sample based on the reference sound field and the transmitted sound field.

[0035] In this step, time-windowing and fast Fourier transform are performed on the pure water reference sound field and the transmitted sound field signal after the sample is inserted to obtain the reference sound pressure spectrum. With transmission sound pressure spectrum Based on the reference acoustic pressure spectrum With transmission sound pressure spectrum The experimental insertion attenuation was calculated based on the amplitude ratio of the two. By using the spectral ratio of the reference sound field to the transmitted sound field, the common system response of the ultrasonic generator, hydrophone, and underwater propagation can be eliminated, and the frequency-related amplitude attenuation and phase change caused by the bone sample itself can be extracted. Subsequently, the insertion attenuation is corrected by combining the transmission coefficient correction term at the interface before and after insertion of the sample and the diffraction correction term caused by finite aperture / finite distance, and then divided by the equivalent propagation thickness L of the sample to obtain the frequency-related total attenuation coefficient. ,in, This is a correction term for the transmission coefficient. This is a diffraction correction term caused by finite aperture / finite distance. If comparing acoustic pressure amplitude spectra, then 20log is used. 10 To calculate the experimental insertion decay; if energy or power spectrum comparison is used, then 10log is used accordingly. 10 To calculate the experimental insertion attenuation, the frequency-dependent measured total attenuation curve is obtained. The total attenuation curve can be expressed in dB / mm as an observation for subsequent porosity inversion.

[0036] Step 204: Establish the relationship between the phase velocities of volume waves in an isotropic homogeneous medium.

[0037] In this step, the quantitative binding relationship between the wave phase velocity of the elastic body and the intrinsic parameters of the medium can be obtained based on the theory of isotropic linear elasticity, for example, through the generalized Hooke's law, providing a basic theoretical constraint for the subsequent modeling of three-phase porous media.

[0038] Specifically, based on the theory of small-strain isotropic linear elasticity, and defined by the generalized Hooke's law:

[0039] Where σ is the stress tensor, and its diagonal terms Indicates normal stress (e.g.) ), off-diagonal terms , , This represents shear stress.

[0040] Shear stress satisfies:

[0041] in, and These are normal strain and shear strain, respectively. For volumetric strain, and Let be Lamé's constant. In an isotropic, homogeneous medium, the Navier wave equation can be obtained by simultaneously applying the momentum conservation equation and the generalized Hooke's law. After decomposing the displacement field into irrotational and rotational components, two types of body waves can be obtained, with corresponding phase velocities: the phase velocity of elastic longitudinal waves (compression waves, P-waves) and the phase velocity of shear waves (S-waves) are: in, and Let Lamé be the constant. It is the equivalent mass density.

[0042] Step 205: Equivalently treat the three-phase mixed medium of the bone sample as an isotropic homogeneous medium and calculate the equivalent parameters.

[0043] In this step, the bone sample is defined as a three-phase mixed medium consisting of a bone mineral phase (s), an intrapore cellular solid phase (h), and a pore fluid phase (w); the overall porosity is assumed to be... The saturation of cellular solids is Define the three-phase volume fraction: Bone mineral phase volume fraction: ; Volume fraction of cellular solid phase: ; Pore ​​fluid phase volume fraction: ; in, , , These represent the volume fractions of the bone mineral matrix, cellular solids, and pore fluid, respectively. Based on Bruggeman's effective medium theory, the volume fractions of each phase ( , , From the single-phase elastic modulus and the equivalent bulk modulus and equivalent shear modulus, we can calculate the equivalent bulk modulus and equivalent shear modulus. The single-phase elastic modulus refers to the material parameter of each constituent phase itself; each phase has its own intrinsic elastic parameter: bulk modulus K. i and shear modulus μ i , K i Let i be the bulk modulus of the i-th phase. To represent the shear modulus of the i-th phase, an equivalent bulk modulus is introduced. and equivalent shear modulus This represents the overall response parameters of the equivalent medium to volumetric compression and shear deformation after macroscopically equating the three-phase mixture to a homogeneous isotropic medium. This leads to the equivalent Lamé constant. For multiphase systems, it can be written as about and The implicit equations typically require numerical iteration to solve. Equivalent bulk modulus With equivalent shear modulus satisfy: ， , .

[0044] The first equation controls the overall resistance to volumetric compression, the second equation controls the overall resistance to shear deformation, and the third equation... It is an auxiliary parameter used when calculating the shear modulus, reflecting... and The interaction, Let i be the volume fraction of the i-th phase in the overall material, and then derive the equivalent Lamé constant. , This is obtained through iterative solutions based on Bruggeman's effective medium theory. The equivalent mass density can also be calculated. ), where equivalent mass density Volume average can be calculated based on volume fraction: ,in, It is the density of the bone mineral matrix, It is the density of cellular solids and It is the pore fluid density.

[0045] Equivalent Lamé constant , and equivalent mass density Substituting these values ​​into the preceding formula for the volume wave phase velocity yields the equivalent volume wave phase velocities: elastic longitudinal wave velocity Vp and shear wave velocity Vs.

[0046] In other embodiments, the wave equation and phase velocity expression can be directly derived based on Cauchy's equation of motion (the first law of continuous medium mechanics) or starting from the conservation of momentum of the infinitesimal elements of the medium, combined with the elastic constitutive relation of the Lamé form.

[0047] Alternatively, based on Hamilton's principle and the conservation of energy, without relying on the differential constitutive equations of stress-strain, the wave equation and the expression for phase velocity can be directly derived through the variational extrema of the kinetic energy and strain energy of the elastic system (the actual motion satisfies the zero variation of the action).

[0048] Step 206: Construct the three-phase hole elastic control equation.

[0049] In this step, the equivalent volume wave phase velocity obtained solely from the aforementioned equivalent parameters does not yet consider the relative motion and viscous dissipation between the pore fluid and the solid framework. To describe the viscous dissipation and tortuosity effect between the pore fluid and the solid framework, the Biot–Johnson–Koplik–Dashen (Biot–JKD) model, also known as the dynamic permeability model, can be used in this embodiment to derive the frequency-dependent permeability:

[0050] in, This is the static permeability. and These are the constants of the Biot–JKD model. ω is the angular frequency, and i is the imaginary unit.

[0051] Substitute the frequency-related permeability into the fluid-solid drag term ( )=- ( ) ( The fluid-structure drag term characterizes the viscous drag of the fluid relative to the skeleton motion. The Biot-JKD model generalizes this fluid-structure drag term from low-frequency constant damping to frequency-dependent damping, where... ( This usually represents the relative flow rate / filtering speed. ( ) is the frequency-dependent drag coefficient.

[0052] This allows us to construct a frequency-dependent fluid-structure drag coefficient to characterize the viscous drag generated when pore fluid moves relative to the skeleton; it manifests as a damping term in the frequency domain governing equations, and therefore can also be considered a frequency-dependent damping coefficient. , in, For pore fluid viscosity, This represents the volume fraction of the pore fluid phase. Because... Since it is a complex function, therefore It is also a frequency-dependent complex function. Through the fluid-structure drag coefficient, the mass matrix and stiffness matrix of the three-phase pore elastic control equation are transformed into complex form, thus reflecting the intrinsic decay in the dispersion equation. The intrinsic decay is the decay caused by the dissipation mechanism inside the material, which is the viscous dissipation / wave-induced fluidflow (WIFF) / pore pressure relaxation caused by the fluid relative to the skeleton.

[0053] In other embodiments, to describe the viscous dissipation and tortuosity effect between the pore fluid and the solid framework, the classical Biot low-frequency model, the Pride–Lafarge dynamic tortuosity / dynamic permeability model, the Biot–Stoll model, or the extended Biot pore viscoelastic model that includes a squirt-flow mechanism can also be used to characterize the fluid-structure interaction dissipation process.

[0054] In the frequency domain, let the displacement amplitude vector of the three-phase medium be: , in, , and These represent the displacement amplitudes of the bone mineral phase, cellular solid phase, and pore fluid phase, respectively.

[0055] The three-phase orifice elastic control equation can be expressed as: , Where M is the mass matrix, This is the frequency-dependent damping matrix. For the elastic recovery operator matrix, This is the displacement amplitude vector of the three-phase medium.

[0056] M is the mass matrix, used to characterize the inertial properties of a three-phase medium. Its data basis includes the three-phase volume fraction, the three-phase equivalent mass density, and the interphase inertial parameters; K( Let B(ω) be the elastic recovery operator matrix, used to characterize the elastic recovery effect of the three-phase medium. Its data basis includes the equivalent bulk modulus, equivalent shear modulus, equivalent Lamé constant, and spatial differential operator terms. Let B(ω) be the frequency-dependent damping matrix, whose data basis includes pore fluid viscosity, pore fluid phase volume fraction, dynamic permeability, and fluid-structure drag coefficient. Since the frequency-dependent damping matrix contains complex frequency-dependent fluid-structure drag coefficients, the three-phase porosity elastic control equation is a complex coefficient equation. Under the simple harmonic wave assumption, the time derivative can be written as... Therefore, the drag term corresponding to the fluid-structure relative velocity can be transformed in the frequency domain into a term related to... The coupling terms are proportional. Therefore, the frequency domain control equations of the three-phase aperture elastic control equations are no longer real coefficient equations, but complex coefficient equations; equivalently, the inertial terms in the matrix of the three-phase aperture elastic control equations ( ), Coupling terms ( ) and elasticity term ( After being standardized, it can be written in complex coefficient form. This three-phase porosity elastic control equation can reflect the internal dissipation (i.e., intrinsic decay) caused by viscous flow of pore fluid, fluid-solid relative motion, and tortuosity effect.

[0057] Step 207: Derive the complex dispersion equation for the propagation mode.

[0058] In this step, for a given frequency By establishing the determinant conditions of the three-phase aperture elastic control equation, the complex wave number is solved. In other words, for a given frequency By substituting the plane wave solution into the three-phase aperture elastic control equation and setting the determinant of the coefficient matrix to zero, the complex dispersion equation for the corresponding propagation mode can be obtained.

[0059] In this step, for a given frequency Assuming the displacement of the three-phase medium along the propagation direction is represented by a plane wave, and substituting it into the three-phase orifice elastic control equations, we obtain a system of homogeneous linear algebraic equations concerning the amplitudes of the three-phase displacements. Let the three-phase displacement amplitude vector be... Then the three-phase hole elastic control equation can be written as: , Where k is the complex wave number, This is the elasticity coefficient matrix corresponding to longitudinal propagation. Let M be the angular frequency and M be the mass matrix. This is the frequency-dependent damping matrix. Let be the displacement amplitude vector of the three-phase medium. For the above equation to have a non-zero solution, the determinant of its coefficient matrix should satisfy:

[0060] This equation is the complex dispersion equation for the corresponding propagation mode. Solving the complex dispersion equation yields the complex wave number k(ω), where the real part characterizes the wave propagation characteristics and the imaginary part characterizes the wave attenuation characteristics. The solution used is a harmonic plane wave that perfectly matches the experimental system described in the preceding steps. ,in, It is the complex vector of the displacement field of a three-phase medium in the frequency domain. The coordinates are one-dimensional spatial coordinates representing the direction of ultrasound propagation. Angular frequency, Let be the complex vector of the displacement amplitude constant of the three-phase medium, e be the base of the natural logarithm, i be the imaginary unit, and k be the complex wave number. Substituting this simple harmonic plane wave solution into the three-phase aperture elastic control equation, we obtain... Replacing it with the algebraic form -ik, and canceling the non-zero exponent terms, the partial differential equation containing the spatial differential operator is transformed into a system of third-order linear homogeneous algebraic equations with respect to only the angular frequency ω and the complex wave number k: A(ω,k). u0=0, where A(ω,k) is a complex coefficient matrix.

[0061] Solving the complex dispersion equation yields the complex wavenumbers for each mode. Or equivalent complex slowness ,in or It is a wave solution, representing the solution at a given frequency. The complex wavenumber / complex slowness of a certain mode is obtained through the dispersion equation, where This yields the complex dispersion equation for the fast compression mode (P1). For each modal root (a solution to the dispersion equation), the wave phase velocity... Intrinsic decay is defined as: , Where R and I represent taking the real part and imaginary part respectively, the real part of the complex wave number describes the spatial propagation characteristics of the wave and determines the phase velocity of the wave, and the elastic longitudinal wave velocity of the equivalent volume wave phase velocity can be used as a screening criterion or identification basis for the complex wave number roots corresponding to the fast compression mode (P1). The intrinsic decay is caused by viscous dissipation and tortuosity. The viscous dissipation and tortuosity are the physical explanation for the intrinsic decay, while the complex roots in the complex dispersion equation represent the intrinsic decay mathematically.

[0062] Step 208: Calculate the scattering loss of the high-frequency band of the ultrasonic signal and construct the scattering attenuation.

[0063] In this step, to address the high-frequency scattering loss caused by the trabecular bone / porous microstructure of the skull, the corresponding scattering model is selected to calculate the scattering attenuation based on the matching relationship between the scatterer size and wavelength. , The frequency of the ultrasonic signal. Porosity.

[0064] For example, a Rayleigh scattering model can be used (suitable for scenarios where the size of the bone sample is much smaller than the wavelength λ): , in, A calibrable coefficient related to porosity. The elastic longitudinal wave velocity Vp is the equivalent volume wave phase velocity. The size of the bone sample; Generalized power-law scattering model (suitable for scenarios where the size of the bone sample is close to the wavelength): , in, The scattering intensity coefficient is... It is a frequency-dependent power, used to describe the sensitivity of attenuation to frequency.

[0065] Step 209: Construct the total inversion decay.

[0066] In this step, the total attenuation It can be represented as: , in, For this mode at frequency Porosity Intrinsic decay under these conditions This refers to the scattering attenuation of high-frequency ultrasonic signals.

[0067] Step 210: Obtain the inverted porosity based on the total attenuation and the measured total attenuation curve.

[0068] In this step, the measured total attenuation curve will be... , and the total decay of the inversion Matching is performed within the selected analysis frequency band (e.g., 0.5 MHz to 20 MHz). Perform smoothing and discrete sampling, and scan the porosity within a preset porosity range. Calculate the corresponding one by one And construct the objective function. Use least squares or other numerical optimization methods to find the... Minimum porosity This is taken as the effective porosity of the sample.

[0069] Using the porosity obtained by the above method as one of the main parameters, the propagation delay, attenuation loss, and phase distortion of ultrasound waves in samples (bone tissue) can be corrected, thereby improving the focusing accuracy and imaging quality in sample (bone) ultrasound imaging, focused ultrasound sound field reconstruction, and neuromodulation. Furthermore, porosity itself, as an important indicator reflecting the state of bone microstructure, can also be used for bone quality assessment, osteoporosis screening, bone repair monitoring, and non-destructive characterization of bone phantoms and porous materials.

[0070] The three-phase porosity elastic control equations of the methods described in this specification can quantitatively invert the effective porosity of a sample (skull), providing a precise, interpretable, and engineering-featured basis for transcranial ultrasound propagation modeling, attenuation and phase compensation, and bone parameter imaging.

[0071] Subsequently, 3D-printed epoxy-alumina porous phantoms with known design porosity can be used to complete the experimental calibration and verification of model parameters. By repeating the above measurement and inversion process at different measurement locations, the porosity distribution in the X–Z plane or three-dimensional space can be obtained, achieving accurate spatial characterization of bone microstructure. This not only provides a decomposition of the mechanism of frequency-related attenuation (viscous / torsional loss and scattering contribution), but also quantitatively inverts the effective porosity of the sample, providing a precise, interpretable, and engineering-feasible basis for ultrasonic propagation modeling, attenuation and phase compensation, and parametric imaging of samples (e.g., skull).

[0072] like Figure 4The diagram shown is a schematic representation of an ultrasound-based sample porosity characterization device according to an embodiment of this specification. The diagram illustrates the logic component structure for executing the above method. In this embodiment, the logic component implementing the above method can be implemented by a general-purpose processor or a specially configured processor. The device specifically includes: Experimental unit 401 is used to obtain the measured total attenuation curve of the sample through experiments; The three-phase porosity elastic control equation generation unit 402 is used to convert the three-phase mixed medium of the sample into an isotropic homogeneous medium to obtain the three-phase porosity elastic control equation. The calculation unit 403 is used to calculate the total attenuation of the ultrasonic signal passing through the sample according to the three-phase aperture elastic control equation; The inversion unit 404 is used to compare the total attenuation with the measured total attenuation curve to determine the porosity of the sample.

[0073] The apparatus described in the embodiments of this specification can be used to invert the porosity of a sample (e.g., bone) and obtain porosity parameters to facilitate the imaging of ultrasonic detection data.

[0074] like Figure 5 The illustration shows a computer device provided in an embodiment of this specification. The methods described in this embodiment can be run on the computer device to implement the functions of the data processing apparatus described in this embodiment. The computer device 502 may include one or more processors 504, such as one or more central processing units (CPUs), each of which can implement one or more hardware threads. The computer device 502 may also include any memory 506 for storing information of any kind, such as code, settings, data, etc. Non-limitingly, for example, the memory 506 may include any type of RAM, any type of ROM, flash memory, hard disk, optical disk, etc. More generally, any memory can use any technology to store information. Further, any memory can provide volatile or non-volatile retention of information. Further, any memory can represent a fixed or removable component of the computer device 502. In one case, when the processor 504 executes associated instructions stored in any memory or combination of memories, the computer device 502 can perform any operation of the associated instructions. Computer device 502 also includes one or more drive mechanisms 508 for interacting with any memory, such as hard disk drive mechanism, optical disk drive mechanism, etc.

[0075] Computer device 502 may also include an input / output module 510 (I / O) for receiving various inputs (via input device 512) and providing various outputs (via output device 514). A specific output mechanism may include a presentation device 516 and an associated graphical user interface (GUI) 518. In other embodiments, the input / output module 510 (I / O), input device 512, and output device 514 may be omitted, and the device may function solely as a computer device within a network. Computer device 502 may also include one or more network interfaces 520 for exchanging data with other devices via one or more communication links 522. One or more communication buses 524 couple the components described above together.

[0076] Communication link 522 can be implemented in any way, such as via a local area network, a wide area network (e.g., the Internet), a point-to-point connection, or any combination thereof. Communication link 522 may include any combination of hardwired links, wireless links, routers, gateway functions, name servers, etc., governed by any protocol or combination of protocols.

[0077] This specification also provides computer-readable instructions, wherein when a processor executes the instructions, the program therein causes the processor to perform the methods described above.

[0078] It should be understood that in the various embodiments of this specification, the sequence number of each process does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of this specification.

[0079] It should also be understood that, in the embodiments of this specification, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, and B existing alone. Additionally, the character " / " in this specification generally indicates that the preceding and following related objects have an "or" relationship.

[0080] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this specification can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this specification.

[0081] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0082] In the several embodiments provided in this specification, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the couplings or direct couplings or communication connections shown or discussed may be indirect couplings or communication connections through some interfaces, devices, or units, or they may be electrical, mechanical, or other forms of connection.

[0083] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of the embodiments described in this specification, depending on actual needs.

[0084] Furthermore, the functional units in the various embodiments of this specification can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0085] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this specification, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this specification. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0086] This specification uses specific embodiments to illustrate the principles and implementation methods of this specification. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this specification. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this specification. Therefore, the content of this specification should not be construed as a limitation of this specification.

Claims

1. An ultrasonic-based method of characterizing the porosity of a sample, the method comprising: include: The measured total decay curve of the sample was obtained through experiments; The three-phase mixed medium of the sample is equivalent to an isotropic homogeneous medium, resulting in a three-phase porosity elastic control equation. The three-phase mixed medium of the sample includes: a sample mineral phase, an intrapore cellular solid phase, and a pore fluid phase. The three-phase porosity elastic control equation is used to describe the dissipation of the coupling between the pore fluid and the sample. The total attenuation of the ultrasonic signal after passing through the sample is calculated based on the three-phase aperture elastic control equation. The porosity of the sample is determined by comparing the total attenuation with the measured total attenuation curve.

2. The method of claim 1, wherein, The three-phase mixed medium of the sample is equivalent to an isotropic homogeneous medium, and the three-phase porosity elastic control equation further includes: The three-phase aperture elastic control equations include the frequency-dependent mass matrix, damping matrix, and elastic recovery operator matrix of the sample.

3. The method of claim 2, wherein, The damping matrix is ​​formed by constructing frequency-dependent fluid-structure drag coefficients using the Biot-JKD model, the Biot low-frequency model, the dynamic tortuosity / dynamic permeability model, or the Biot-Stoll model.

4. The method of claim 3, wherein, The coupling between the pore fluid and the sample includes viscous dissipation and tortuosity effects.

5. The method of claim 4, wherein, The three-phase mixed medium of the sample is equivalent to an isotropic homogeneous medium, and the three-phase porosity elastic control equation further includes: Based on the Biot–JKD model, the frequency-dependent dynamic penetration rate is obtained; Substituting the dynamic permeability into the fluid-solid drag term yields the frequency-dependent fluid-solid drag coefficient.

6. The method of claim 5, wherein, The calculation of the total attenuation of the ultrasonic signal after passing through the sample, based on the three-phase aperture elastic control equation, further includes: Based on the volume fractions and single-phase elastic moduli of the sample mineral phase, cellular solid phase within the pores, and pore fluid phase, the equivalent bulk modulus, equivalent shear modulus, and equivalent mass density, which are equivalent to an isotropic homogeneous medium, are calculated. Substituting the equivalent bulk modulus, equivalent shear modulus, and equivalent mass density into the wave velocity-related formula yields the equivalent volume wave phase velocity, which includes the elastic longitudinal wave velocity. For a given frequency, substitute the plane wave solution into the three-phase aperture elastic control equation, and set the determinant of the coefficient matrix of the three-phase aperture elastic control equation to zero to obtain the complex dispersion equation of the propagation mode. Solving the complex dispersion equation yields the complex wave number; wherein, the real part of the complex wave number describes the spatial propagation characteristics of the wave and determines the phase velocity of the wave, the phase velocity being constrained by the elastic longitudinal wave velocity of the equivalent volume wave phase velocity, and the imaginary part of the complex wave number describes the amplitude attenuation characteristics of the wave and determines the intrinsic attenuation of the wave after passing through the sample.

7. The method of claim 6, wherein, Based on Bruggeman's effective medium theory, the equivalent bulk modulus, equivalent shear modulus, and equivalent mass density of the sample, which are equivalent to an isotropic homogeneous medium, are calculated using the volume fractions and single-phase elastic moduli of the sample's mineral phase, cellular solid phase, and pore fluid phase.

8. The method of claim 6, wherein, The relationship related to wave speed is determined based on the generalized Hooke's law.

9. The method of claim 6, wherein, The calculation of the total attenuation of the ultrasonic signal after passing through the sample, based on the three-phase aperture elastic control equation, further includes: Based on the scattering loss caused by the sample in the high-frequency band of the ultrasonic signal, a scattering attenuation is constructed; The total attenuation is formed by combining the scattering attenuation and the intrinsic attenuation.

10. The method of claim 9, wherein, Based on the scattering loss caused by the sample in the high-frequency band of the ultrasound signal, the construction of scattering attenuation further includes: The scattering attenuation is constructed using a Rayleigh-type algorithm; or, The scattering attenuation is constructed using a generalized power-law algorithm.

11. The method of claim 1, wherein, Determining the porosity of the sample by comparing the total attenuation with the measured total attenuation curve further includes: The total attenuation is fitted to the measured total attenuation curve, and an objective function is constructed with the goal of minimizing the error. The porosity corresponding to the minimum objective function is taken as the porosity of the sample.

12. An ultrasound-based sample porosity characterization apparatus, characterized by, include: Experimental unit, used to obtain the measured total decay curve of the sample through experiments; The three-phase porosity elastic control equation generation unit is used to convert the three-phase mixed medium of the sample into an isotropic homogeneous medium to obtain the three-phase porosity elastic control equation. The calculation unit is used to calculate the total attenuation of the ultrasonic signal after passing through the sample according to the three-phase aperture elastic control equation; The inversion unit is used to compare the total attenuation with the measured total attenuation curve to determine the porosity of the sample.

13. A computer device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1-11.

14. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the method of any one of claims 1-11.

15. A computer program product, characterised in that, The computer program product includes a computer program that, when executed by a processor, implements the method according to any one of claims 1-11.

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